This course is an introduction to differential equations, with particular emphasis on scientific applications. Topics we will cover include homogeneous and nonhomogeneous linear equations, systems of equations, the Laplace transform, series solutions to equations and nonlinear systems. Numerical and graphical methods will play an important role throughout the semester; these will be implemented using a variety of computer and calculator technologies. The prerequisite is completion of one of the standard calculus sequences (either MAT 125-127 or MAT 131-132). The 200-level courses MAT 203/205 (Calculus III) and MAT 211 (Linear Algebra) are not required, but it is strongly recommended that you have had some exposure to basic ideas in multivariable calculus and linear algebra.
Approximately twice a month there will be a short quiz, usually administered during a lecture section.
Late homeworks will not be accepted except under very exceptional
circumstances. Likewise, no late quizzes will be given. At the end of
the semester, I will drop your lowest homework and your lowest quiz
grade.
Grading Policy:
Grades will be computed according to the following percentages:
| Homework | 20% |
| Quizzes | 10% |
| First Midterm (February 21 in class) | 20% (will cover 1.1-2.3) |
| Second Midterm (April 4 in class) | 20% (will cover 2.4-4.1) |
| Final (Tuesday, May 14 8:00-10:30am) | 30% (cumulative) |
No make-up exams will be given. If a midterm exam is missed because of a serious (documented) illness or emergency, your semester grade will be determined on the basis of other work done in the course. Exams missed for other reasons will be counted as failures.
Resources: If you have questions regarding the course material at any time during the semester, you are encouraged to send email, either to myself or to the TA. It is not always easy to explain mathematical concepts via email, however, so if your question is a mathematical one, you should probably ask me in person during my office hours. Another excellent source of help is the Mathematics Learning Center (A-125 in the Physics Building), which is staffed by advanced math majors and graduate students daily. For a schedule of their hours, check their website.
Students with Disabilities: If you have a physical,
psychological, medical, or learning disability that may impact on your
ability to carry out assigned course work, you are strongly urged to
contact the staff in the
Disabled
Student Services (DSS) office: Room 133 in the Humanities
Building; 632-6748/TDD. DSS will review your concerns and determine,
with you, what accommodations are necessary and appropriate. All
information and documentation of disability is confidential.
Arrangements should be made early in the semester so that your needs
can be accommodated.
| Week of | Topics | Assigned problems | Suggested additional problems |
|---|---|---|---|
| Jan. 21 | 1.1: Mathematical Models |
1.1: 6,10,16,24,34,40 |
1.1: 9,11,15,21,31,35 |
| Jan. 28 | 1.2: General an Particular Solutions 1.3: Direction Fields 1.4: Separable Equations |
1.2: 6,8,16,22 1.3: 14,18,25,26 1.4: 4,12,22,46,48 |
1.2: 5,7,17,23 1.3: 2,11,17,23,24,33 1.4: 13,25,43,49 |
| Feb. 4 | 1.5: Linear First-Order Equations 1.6: Substitution Methods and Exact Equations |
1.5: 2,12,24,36 1.6: 12,34,38,54,55 |
1.5: 3,9,23,35 1.6: 3,9,13,17,31,37 |
| Feb. 11 | 2.1: Population Models 2.2: Equilibrium Solutions |
2.1: 3,11,12,20 2.1: Computing Project, parts A and B 2.2: 2,9,21 |
2.1: 1,18 2.2: 1,3,11 |
| Feb. 18 First midterm exam on 02/21 |
2.3: Acceleration-Velocity Models | 2.3: 2,4,10,22,23 | 2.3: 3,5,11,20 |
| Feb. 25 | 2.4: Euler's Method 2.5: More on Euler's Method 2.6: The Runge-Kutta Method |
2.4: 4,8,13 2.6: 3,8 |
2.4: 10,14 2.6: 4,10 |
| March 4 | 3.1: Second-Order Linear Equations 3.2: General Solutions of Linear Equations |
3.1: 4,10,14,34,40,46 3.2: 4,9,16,30 |
3.1: 3,9,15,39,45 3.2: 1,7,13,27 |
| March 11 | 3.3: Homogeneous Equations with Constant Coefficients 3.4: Mechanical Vibrations |
3.3: 8,24,40 3.4: 2,4,10,20,22 |
3.3: 9,15,25 3.4: 1,3,15,17 |
| March 18 | 3.5: Nonhomogeneous Equations 3.6: Forced Oscillations and Resonance |
3.5: 6,14,20,38,55 3.6: 4,19 |
3.5: 3,17,33,49 3.6: 1 |
| April 1 Second midterm exam on 04/04 |
4.1: First-Order Systems of Equations | 4.1: 2,8,14,18,23 | 4.1: 1,7,11,15 |
| April 8 |
4.2: The Method of Elimination 5.1: Matrices and Linear Systems |
4.2: 8,10,22 5.1: 4,9,14,20,24,33 |
4.2: 3,9,21 5.1: 3,6,10,13,19,23,32 |
| April 15 | 5.2: The Eigenvalue Method 5.4: Multiple Eigenvalue Solutions |
5.2: 4,12,18,30,38 5.4: 2,8,12,20 |
5.2: 1,7,13,17,29 5.4: 1,3,7,13 |
| April 22 | 7.1: Introduction to Laplace Transforms 7.2: Transformation of Initial value Problems |
7.1: 1,4,8,14,20,38 7.2: 4,10,12,20,28 |
7.1: 3,7,13,19,37 7.2: 3,9,19,29 |
| April 29 | 6.1: The Phase Plane 6.2: Linear and Almost Linear Systems |
6.1: 1,3,5,7 6.2: 11,14,17 |
6.1: 2,4,6,8 6.2: 13,15,17 |
| May 6 | Review | - | - |